In a medium mixing bowl, combine water, oil, sugar, yeast, salt and whole wheat flour with a wooden spoon until combined and smooth. Stir in all-purpose flour until the mixture comes together into a shaggy mass.
With clean hands, knead the dough in the bowl for 10 minutes until it becomes smooth and very elastic, adding very small amounts of extra flour if dough is extremely sticky. Alternatively, knead dough at a low speed in a stand mixer fitted with a dough hook attachment until it is very elastic and smooth, about 8 minutes.
Turn dough out onto a lightly floured work surface and form into a smooth ball. Lightly oil a clean mixing bowl and place dough inside, then rub oiled hands over the top of the dough.
Cover bowl with a damp cloth and let rise in a warm place for 1 hour.
Meanwhile, place a baking stone or large cast iron skillet on the top oven rack and preheat oven to 500o F.
Punch down the dough, transfer to a lightly floured work surface and cut into 6 even pieces. Form each dough piece into an even ball. Cover with a damp towel and let rest for 10 minutes.
Roll each piece of dough into a 6-inch wide circle. Place on a lightly floured tray. Cover and place in a warm spot to rise for about 15 minutes.
Bake in batches until pitas have puffed and begin to brown, about 3-4 minutes.
Place baked pita in a napkin or towel-lined basket. Serve warm.
A traditional pita. Can be served as a flatbread or used for a pocket bread sandwich.
1tablespoonextra virgin olive oilplus ¼ teaspoon
1packageactive dry yeast, about 2 ¼ teaspoons
½cupwhole wheat flour
2cupall-purpose flourplus a little extra for dusting